Entire solutions of a functional equation

Abstract

The aim of the present note is to show that all entire solutions f : C → C, of order less than 4, of the equation |f(s + it)f(s - it)| = |f(s)[2] - f(it)[2]|, s,t ϵ R are given by f(z) — az and f(z) = a sin bz, where a, b are arbitrary complex constants. This is a partial solution of the problem posed by Themistocles M. Rassias [3] (see also [4]).